Answer:
Real and irrational root
Step-by-step explanation:
Since a quadratic equation [tex]ax^2+bx+c[/tex],
Has two real different roots,
If the value of discriminant [tex]D=b^2-4ac>0[/tex]
Has two equal real roots,
If [tex]D=0[/tex]
Has two imaginary roots,
If [tex]D<0[/tex]
Here, the given equation,
[tex]x^2-5x-4=0[/tex]
[tex]D=(-5)^2-4\times 1\times -4=25+16= 41>0[/tex]
Hence, the equation has the two unequal real roots,
Now, √D is an irrational number ( Which can not be expressed in the form of p/q in which q≠0 )
Therefore, the given equation has real and irrational root,
Third option is correct.
